Related papers: Sampling Theorem and explicit interpolation formul…
We obtain polynomial decay rates for $C_{0}$-semigroups, assuming that the resolvent grows polynomially at infinity in the complex right half-plane. Our results do not require the semigroup to be uniformly bounded, and for unbounded…
Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of…
We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse…
In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…
We prove decay estimates for solutions to non-isotropic linear systems of wave equations. The defining feature of these estimates is that they depend only on the commutation properties of the system with the scaling vector field. As…
A closed-form formula for the nonlinear interference estimation of arbitrary modulation formats in ultra-wideband transmission systems is presented. Enabled by the proposed approach, the formula is applied to the entire S+C+L band (20 THz)…
The work concerns about multiscale McKean-Vlasov stochastic systems. First of all, we prove an average principle for these systems in the $L^2$ sense. Moreover, a convergence rate is presented. Then we define the nonlinear filtering of…
Slice sampling is an efficient Markov Chain Monte Carlo algorithm to sample from an unnormalized density with acceptance ratio always $1$. However, when the variable to sample is unbounded, its "stepping-out" heuristic works only locally,…
Resonant upconversion through a sixth order relativistic nonlinearity resulting in a unique resonance was recently proposed [V. M. Malkin and N. J. Fisch, Physical Review E 108, 045208 (2023)]. The high order resonance is a unique…
Using Coherent-State (CS) techniques, we prove a sampling theorem for holomorphic functions on the hyperboloid (or its stereographic projection onto the open unit disk $\mathbb D_1$), seen as a homogeneous space of the pseudo-unitary group…
We study the spectral behavior as the sample size $n \to +\infty$ of integral operators defined by convolution of a non-negative symmetric kernel k with respect to empirical measures $\mu_n = \frac{1}{n} \sum_{i=1}^n \delta_{X_i}$, where…
Smoothing splines are twice differentiable by construction, so they cannot capture potential discontinuities in the underlying signal. In this work, we consider a special case of the weak rod model of Blake and Zisserman (1987) that allows…
Substantially extending previous results of the authors for smooth solutions in the viscous case, we develop linear damping estimates for periodic roll-wave solutions of the inviscid Saint-Venant equations and related systems of hyperbolic…
Partial sum rules are widely used in physics to separate low- and high-energy degrees of freedom of complex dynamical systems. Their application, though, is challenged in practice by the always finite spectrometer bandwidth and is often…
We establish error bounds of the Lie-Trotter splitting ($S_1$) and Strang splitting ($S_2$) for the Dirac equation in the nonrelativistic limit regime in the absence of external magnetic potentials, with a small parameter $0<\varepsilon\leq…
We show that a broad class of signal acquisition schemes can be interpreted as recording data from a signal $x$ in a space $\cal U$ (typically, though not exclusively, a space of bandlimited functions) via an orthogonal projection $w =…
It is a fundamental principle of quantum theory that an unknown state cannot be copied or, as a consequence, an unknown optical signal cannot be amplified deterministically and perfectly. Here we describe a protocol that provides…
We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem requires less than half…
We experimentally demonstrated entanglement extraction scheme by using photons at the telecommunication band for optical-fiber-based quantum communications. We generated two pairs of non-degenerate polarization entangled photons at 780~nm…
Nonleptonic $\Omega^{-}$ decay branching ratios are estimated by means of the QCD enhanced effective weak Hamiltonian supplemented by the SU(3) Skyrme model used to estimate the nonperturbative matrix elements. The model has only one free…